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Algebra II Period:____ Name:___________________________ Mr. Leo

Study Guide for Unit 1: Functions (Part II of II) This study guide covers sections 1.6 through 1.10. (1.6; Linear functions) 1. Nicole’s Cow-Cars rents cars for a flat fee of $450 plus $0.40 for each mile traveled. a. Write a linear function that describes the cost of a rental from Nicole’s Cow-Cars as a function of miles traveled. b. What is the slope of your function? What is the y-intercept? c. How much money would it cost to drive 250 miles? d. How many miles would you need to drive for the total cost to be $490? (1.9; Inverse functions) 2. Find the inverse of the function 𝑓 𝑥 = 𝑥 + 15.

TRUE GRIT WON’T QUIT

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(1.6; Linear functions) 3. Write a function that describes the table below.

𝒙 𝒃(𝒙) 0 -4 1 5 2 14 3 23 4 32

(1.6; Linear functions) (1.10; Inverse functions in the real world) 4. Tony has $6 in his wallet. He spends $0.50 each day for 10 days in a row. a. What is the y-intercept (starting value) of this situation? b. What is the slope (rate of change) of this situation? c. Graph the situation below.

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d. Find 𝑓(4) and interpret it in the real-world context of the situation. __________________________________________________________________________________

__________________________________________________________________________________ e. Find 𝑓!!(2) and interpret it in the real-world context of the situation. __________________________________________________________________________________

__________________________________________________________________________________

(1.6; Linear functions & 1.9; Inverse functions) 5. Mr. Leo’s little brother is 110 cm tall. He grows 16 cm every 2 years. Write a function to express his height, where 𝑦 represents his height and 𝑥 represents the number of years that have passed since he was 110 cm tall. 6. a. Graph the function 𝑓 𝑥 = !

!𝑥 − 6 on the coordinate plane below.

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b. Ms. Lopez tells you that the inverse of 𝑓 𝑥 = !

!𝑥 − 6 is the function 𝑔 𝑥 = !

!𝑥 + 9. Is

Ms. Lopez right? Show the work that led you to this conclusion. [Hint: Test an input.] (1.85; Function composition) 7. If 𝑓 𝑥 = 2𝑥 and 𝑔 𝑥 = 3𝑥 − 8, which composition – 𝑓(𝑔 𝑥 ) or 𝑔(𝑓 𝑥 ) – will give you the function 6𝑥 − 16? Show all your work. (1.7; Reading function graphs) 8. Over what values of x is this function decreasing?

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(1.85; Function composition) (1.9; Inverse functions) 9. Consider the function 𝑓 𝑥 = !

!+ 3.

a. Find the inverse of 𝑓(𝑥). b. Compose 𝑓(𝑥) with its inverse [In other words, find 𝑓(𝑓!! 𝑥 ).] c. What do you get every time you compose a function with its inverse? (1.85; Function composition) 10. If 𝑓 𝑥 = 4𝑥 − 3 and 𝑔 𝑥 = 𝑥! + 2𝑥, which composition – 𝑓(𝑔 𝑥 ) or 𝑔(𝑓 𝑥 ) – will give you the function 16𝑥! − 16𝑥 + 3? Show all your work.

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(1.9; Inverse functions)

11. Find the inverse of the function 𝑔 𝑥 = !!!!!

(1.6; Linear functions) 12. Consider the linear function below:

a. What does x equal at the y-intercept? (This is true for every function.) _______ b. What does y equal at the x-intercept? (This is true for every function.) _______ c. Find the x- and y-intercepts of 3𝑥 + 6𝑦 = 12 by… i) Using the graph above ii) Using algebra d. For what value of 𝐴 will 𝐴𝑥 + 5𝑦 = 20 have an x-intercept of 10?